Positioning systems used by modern mobile devices use time-of-arrival (TOA) to estimate the distance between a wireless transmitter and wireless receiver. TOA-based techniques estimate the propagation delay of radio frequency (RF) signals arriving on a direct line-of-sight (LOS) path between the wireless transmitter and wireless receiver. For outdoor environments where there are few buildings, the TOA can be accurately estimated. For indoor and dense urban areas that suffer from severe multipath conditions, the TOA is difficult to determine accurately. In these multipath environments, multiple echoes of the transmitted RF signal are received by the wireless receiver. If the RF signal is wideband (i.e., has short transition times), the echoes are separable and the delay to the first echo can be measured by the wireless receiver. However, for narrowband signals, for which the rise time can be much longer than the TOA difference between the echoes, it is difficult for the wireless receiver to distinguish the echoes from each other.
The effect of multipath can be estimated from a frequency spectrum of the received RF signal. Assuming a known transmitted RF signal, the frequency spectrum of the received RF signal will equal the product of the known frequency spectrum of the transmitted RF signal and the frequency response (magnitude and phase) of the multipath channel. For wideband signals, inverse frequency transform techniques can be used to estimate the delays and magnitudes of the echoes, from which the propagation delay can be estimated as the delay from the first echo. For narrowband signals, complex methods can be used to estimate the propagation delay.